A tornado-scale vortex in the tropical cyclone (TC) boundary layer (TCBL)
has been observed in intense hurricanes and the associated intense turbulence
poses a severe threat to the manned research aircraft when it penetrates
hurricane eyewalls at a lower altitude. In this study, a numerical experiment
in which a TC evolves in a large-scale background over the western North
Pacific is conducted using the Advanced Weather Research and Forecast (WRF)
model by incorporating the large-eddy simulation (LES) technique. The
simulated tornado-scale vortex shows features similar to those revealed with
limited observational data, including the updraft–downdraft couplet, the
sudden jump of wind speeds, the location along the inner edge of the eyewall,
and the small horizontal scale. It is suggested that the WRF–LES framework
can successfully simulate the tornado-scale vortex with grids at a
resolution of 37 m that cover the TC eye and eyewall.

The simulated tornado-scale vortex is a cyclonic circulation with a small
horizontal scale of ∼1 km in the TCBL. It is accompanied by strong
updrafts (more than 15 m s−1) and large vertical components of
relative vorticity (larger than 0.2 s−1). The tornado-scale vortex
favorably occurs at the inner edge of the enhanced eyewall convection or
rainband within the saturated, high-θe layer, mostly below
an altitude of 2 km. In nearly all the simulated tornado-scale vortices,
the narrow intense updraft is coupled with the relatively broad downdraft,
constituting one or two updraft–downdraft couplets, as observed by the
research aircraft. The presence of the tornado-scale vortex also leads to
significant gradients in the near-surface wind speed and wind gusts.

Tropical cyclones (TCs) pose a severe risk to life and property in TC-prone
areas and the risk will increase due to the rapidly rising coastal population
and number of buildings (Pielke et al., 2008; Zhang et al., 2009). One of the major TC
threats is damaging winds. Uneven damage patterns often show horizontal
scales ranging from a few hundred meters to several kilometers (Wakimoto and
Black, 1994; Wurman and Kosiba, 2018), suggesting that TC threats are
associated with both sustained winds and gusts. The latter are believed to
result from small-scale coherent structures in the TC boundary layer (Wurman
and Winslow, 1998; Morrison et al., 2005; Lorsolo et al., 2008; Kosiba et
al., 2013; Kosiba and Wurman, 2014). The small-scale coherent structures may
have significant implications for the vertical transport of energy in TCs and
thus TC intensity and structure (Zhu, 2008; Rotunno et al., 2009; Zhu et al.,
2013; Green and Zhang, 2014, 2015; Gao et al., 2017). While understanding of
the coherent structure is very important for mitigating TC damage and
understanding of TC intensity and structure changes, for now direct in situ
observation and remote-sensing measurements can only provide very limited
information.

Another important small-scale feature is the so-called eyewall vorticity
maximum (EVM) (Marks et al., 2008) or tornado-scale vortices in the TCBL
(Wurman and Kosiba, 2018; Wu et al., 2018). So far, our understanding is
mainly from a few observational analyses based on limited data collected
during the research aircraft penetration of hurricane eyewalls. A WP-3D
research aircraft from National Oceanic and Atmospheric Administration (NOAA)
encountered three strong updraft–downdraft couplets within 1 min while
penetrating the eyewall of category 5 Hurricane Hugo (1989) at 450 m
in altitude (Marks et al., 2008). The severe turbulence caused the failure of
one of the four engines and the people on board were at a severe risk. The
aircraft finally escaped with the help of a U.S. Air Force reconnaissance
WC-130 aircraft, which found a safe way out through the eyewall on the
northeast side of Hugo. Since then aircraft missions have been prohibited
in the boundary layer of the TC eyewall. Later analysis indicated that the
dangerous turbulence was associated with a tornado-scale vortex, which is
comparable to a weak tornado in terms of its diameter of about 1 km and the
estimated peak cyclonic vorticity of 0.125 s−1 (Marks et al., 2008).
Such strong turbulence was also observed in Hurricanes Isabel (2003) and
Felix (2007) below 3 km (Aberson et al., 2006, 2017). So
far, little is known about the structure and evolution of the tornado-scale
vortex.

With advances in numerical models and computational capability, the large-eddy simulation (LES) technique has been incorporated into the Advanced
Weather Research and Forecast (WRF) model (Mirocha et al., 2010) and an
increasing number of TC simulations have been conducted with horizontal grid
spacing of less than 1 km (Zhu, 2008; Rotunno et al., 2009; Bryan et al., 2014;
Stern and Bryan, 2014; Rotunno and Bryan, 2014; Green and Zhang, 2015). In
LES, the energy-producing scales of three-dimensional (3-D) atmospheric
turbulence in the planetary boundary layer (PBL) are explicitly resolved,
while the smaller-scale portion of the turbulence is parameterized (Mirocha
et al., 2010). Effort has been made to simulate the structure of the TC PBL
eddies and the associated influence on TC intensity. Zhu (2008) simulated the
structure of the coherent large-eddy circulations and the induced vertical
transport using the WRF–LES framework with horizontal resolutions of 300
and 100 m. When the horizontal resolution was increased from 185 to 62 m on
the f plane, Rotunno et al. (2009) found a sharp increase in randomly
distributed small-scale turbulent eddies, while 1 min mean TC intensity
began to decrease. Green and Zhang (2015) performed several 6 h one-way
simulations of Hurricane Katrina (2005) without a boundary layer
parameterization (horizontal resolutions of 333, 200, and 111 m). Rotunno et
al. (2009) and Green and Zhang (2015) suggest that the horizontal resolution
should be below 100 m to simulate the development of 3-D turbulent eddies in
the
TCBL. Ito et al. (2017) found that the near-surface coherent structures can
be successfully simulated by using the horizontal resolution of 70 m, which
appears to be caused by an inflection-point instability of both radial and
tangential winds.

It is clear that understanding of the tornado-scale vortex would enhance the
safety of flights into very intense TCs. In addition, tornado-scale
vortices may contribute to TC intensification by mixing the high-entropy air in
the eye into the eyewall (Persing and Montgomery, 2003; Montgomery et al.,
2006; Aberson et al., 2006). By simulating tornado-scale vortices in the
TCBL, this study will particularly focus on the spatial distribution of
occurrence of the tornado-scale vortices and the features of their 3-D structures.

In this study a semi-idealized numerical simulation is conducted using
version 3.2.1 of the WRF model. Following Wu and Chen (2016), two steps were
taken to construct the initial conditions for the numerical experiment. A
symmetric vortex was first spun up without the environmental flow on an
f plane for 18 h and then the vortex was embedded in the large-scale
background of Typhoon Matsa (2005) from 00:00 UTC 5 August to 12:00 UTC
6 August. The large-scale environment was derived from the National Centers
for Environmental Prediction (NCEP) Final (FNL) Operational Global Analysis
data with resolution of 1.0∘× 1.0∘ using a 20-day
low-pass Lanczos filter (Duchon, 1979).

The spun-up vortex is initially located at the center of Typhoon Matsa
(25.4∘ N, 123.0∘ E). The outermost domain (centered at
30.0∘ N, 132.5∘ E) covers an area of 6210 km × 5170 km
with a horizontal grid spacing of 27 km. The numerical experiment is
designed with six two-way interactive domains embedded in the 27 km
resolution domain to simulate energetic three-dimensional turbulent eddies in the
TC eyewall and their influence on the TC vortex, mesoscale rainbands, and
convective clouds. The horizontal spacing decreases by a factor of 3 with the
domain level. The corresponding horizontal resolutions are 9 km, 3 km,
1 km, 1∕3 km (333 m), 1∕9 km (∼111 m), and 1∕27 km (∼37 m) and the numbers
of their grid meshes are 230×210, 432×399, 333×333,
501×501, 1351×1351, and 2431×2431, respectively. The
innermost domain covers the inner region of the simulated TC (90×90 km), including the eye and eyewall. Except for the 27 and 9 km
resolution domains, the other domains move with the TC. The model consists of
75 vertical levels (19 levels below 2 km) with a top of 50 hPa. All lands
in the model are removed and the experiment is run over the open ocean with a
constant sea surface temperature of 29 ∘C.

The physics options used in the simulation are as follows. The Kain–Fritsch
cumulus parameterization scheme and the WRF single-moment three-class scheme are
used in the outermost domain (Kain and Fritsch, 1993). The WRF six-class scheme
is selected in the nested domains with no cumulus parameterization scheme
(Hong and Lim, 2006). The Rapid Radiative Transfer Model (RRTM) and the
Dudhia shortwave radiation scheme are used for calculating long-wave
radiation and shortwave radiation (Mlawer et al., 1997; Dudhia, 1989). The
LES technique is used in the sub-kilometer domains (Mirocha et al., 2010) and
the Yonsei University scheme is adopted for PBL parameterization in the other
domains (Noh et al., 2003).

The model is run for 36 h and the 1∕9 km resolution and
1∕27 km resolution domains are activated at 24 h. In the following
analysis, we will focus on the hourly output from 26 to 36 h. The TC center
is determined with a variational approach in which it is located until the
maximum azimuthal mean tangential wind speed is obtained (Wu et al., 2006).

The simulated TC takes a north-northwest track (not shown). Figure 1 shows
its intensity in terms of the maximum instantaneous and azimuthally averaged
wind speeds at 10 m in the 1∕27 km resolution domain. The instantaneous
winds are obtained directly from the model output without any time averaging.
The azimuthal wind speed is the wind speed averaged azimuthally with respect
to the TC center. The instantaneous maximum wind speed fluctuates between
61.8 and 76.6 m s−1 during the 12 h period, while the fluctuations in
the azimuthal maximum wind speed are relatively small, ranging from 43.5 to
48.8 m s−1. In particular, the TC maintains the azimuthal mean maximum
wind speed of ∼45 m s−1 after the innermost domain has been
activated for 2 h.

Figure 2a shows the simulated 500 m radar reflectivity at 27 h, indicating
that the eyewall is open to the south of the TC center. We examine the radar
reflectivity field and find that the opened eyewall persists during the 10 h
period (not shown). In addition, the location of the enhanced convection
relative to the TC center is generally steady. It is well known that the
eyewall asymmetry is associated with the vertical shear of the environmental
flow (Frank and Ritchie, 2001; Braun and Wu, 2007). In this study the
vertical wind shear is calculated as the difference of wind vectors between
200 and 850 hPa within a radius of 300 km. As shown in the figure, the mean
shear is 7.0 m s−1 to the southeast over the 10 h period. In
agreement with the previous studies, the enhanced eyewall reflectivity is
generally observed in the downshear left side. There are relatively small
changes in the radius of maximum wind (RMW) during the 10 h period, ranging from 28.2 to 30.7 km
at 500 m.

Figure 2Simulated radar reflectivity (dBZ) at 500 m (a) and wind
speed (m s−1) at 10 m (b) within an area of 80 km × 80 km
at 27 h. The plus signs and solid circles indicate the TC center and the
radius of maximum wind at 500 m. The red dots indicate locations of
tornado-scale vortices. The rectangle shows the area used in Fig. 3a. The
arrow shows the vertical wind shear of 7.0 m s−1 between 200 and
850 hPa.

Using the fine-scale dual Doppler data in the right front quadrant and eye of
Hurricane Frances (2014) as it made landfall in Florida, Kosiba and
Wurman (2014) found linear coherent structures with a wavelength of
400–500 m near the surface. Figure 2b shows the simulated near-surface
(10 m) wind speeds in the inner region at 27 h. The instantaneous wind
speed is dominated by quasi-linear coherent structures in the eyewall region.
The intense instantaneous wind speeds coincide with the TC-scale
shear-induced enhanced eyewall convection shown in Fig. 2a. In order to clearly show
the quasi-linear features, we plot the instantaneous wind speed in an
area of 10 km × 7 km at this time (Fig. 3a). The small area is located in
the eyewall to the east of the TC center (Fig. 2b). The streaks of
alternating high and low wind speeds can be clearly seen and are roughly
aligned with the TC-scale flow with an outward angle. We can see that the
instantaneous wind speed exhibits large gradients across the streaks.

Figure 3(a) 10 m wind speed (m s−1) and wind vectors and
(b) the perturbation wind vectors and vertical component of relative
vorticity (shading) at 500 m in the area shown in Fig. 2b. The straight line
is the location of the vertical cross section in Fig. 7 and M2701 and M2705
are the two tornado-scale vortices in the small area. The blue dots indicate
their locations.

Figure 3b shows the perturbation wind field at 500 m in the small area. The
perturbation winds are obtained by subtracting an 8 km moving mean. We
compared the perturbation winds with different sizes of the moving window.
While the perturbation wind fields are very similar, the maximum wind speeds
generally increase with the increasing window size. When the window size is
larger than 8 km, there is little change in the perturbation wind speed. The
simulated small-scale circulations are similar to those found from instead
calculating the perturbations by subtracting the symmetric and
wavenumber 1–3 components with respect to the TC center (not shown). In the
perturbation wind field, we can see two small-scale cyclonic circulations.
The most distinct one has a diameter of ∼2 km. In the next section,
the two cyclones are identified as two tornado-scale vortices (M2701 and
M2705). In the study, the simulated tornado-scale vortex is named with four
digits. While the first two digits indicate the hours of the simulation, the
last two digits show the series number at the same hour. Comparing Fig. 3a and
b indicates that the two tornado-scale vortices also correspond to enhanced
wind speeds at 10 m.

As mentioned in Sect. 1, analyses of a few real cases in intense Atlantic
hurricanes indicate that the tornado-scale vortex is a small-scale feature
that occurs in the turbulent TC boundary layer, with vertical motion and
relative vorticity extremes. Aberson et al. (2006, 2017)
analyzed the extreme updrafts in Hurricanes Isabel (2003) and Felix (2007)
and suggested that the strong updrafts were likely associated with a small-scale vortex. The updraft of 22 m s−1 in Isabel was detected by a GPS
dropwindsonde at just about 1300 m (Aberson et al., 2006; Stern and Bryan,
2018), while the updraft of 31 m s−1 in Hurricane Felix (2007) was
observed at the flight altitude (∼3 km). Marks et al. (2008) found
that the EVM in Hurricane Hugo (1989) was associated with a maximum vertical
motion of 21 m s−1 and a maximum vertical relative vorticity of
0.125 s−1 at the altitude of 450 m. Based on these studies, a small-scale vortex associated with extreme wind speed can be treated
as a
tornado-scale vortex (Wurman and Kosiba, 2018; Wu et al., 2018). The
tornado-scale vortex in the simulated TC is subjectively defined as a
small-scale cyclonic circulation with the diameter of 1–2 km below the
altitude of 3 km, containing maximum upward motion larger than
20 m s−1 and maximum vertical relative vorticity larger than
0.2 s−1. The grid points that satisfy the thresholds of vertical motion
and vertical relative vorticity belong to the same tornado-scale vortex if
they are within a distance of 1 km in the horizontal or vertical directions.
We detect the tornado-scale vortices using the output at 1 h intervals
from 26 to 36 h. A few variables are also stored at 3 s intervals during a
22 min period starting at 30 h.

There are 24 tornado-scale vortices identified at the 11 hourly output times
(Table 1). There are four tornado-scale vortices with maximum vertical
motion of more than 30 m s−1 and maximum vertical component of
relative vorticity larger than 0.4 s−1. Except for the two
tornado-scale vortices at 36 h, the others occur during 26–31 h with 10
cases at 27 h. The lull period is coincident with a relatively weaker
instantaneous maximum wind speed at 10 m, although there is little difference
in the azimuthal mean maximum wind speed (Fig. 1). Examination indicates that
the 10 m instantaneous wind speed maximum at 27 h is associated with M2701.
It is suggested that the tornado-scale vortex can lead to the strongest wind
gust in a TC.

Table 1List of the identified tornado-scale vortices in the TCBL with the
maximum updraft (m s−1) and vertical relative vorticity (s−1) and
the corresponding altitudes (m) in the parentheses. The location column lists
the radial distance from the TC center and the relative distance to the
500 m radius of maximum wind in the parentheses. The Richardson number
(Ri) is averaged over the layer between 200 and 800 m within a radius
of 1.5 km. The four strongest EVMs are indicated in bold.

Some previous studies argued that the presence of mesovortices intensifies
the TC by mixing the high-entropy air in the eye into the eyewall (Persing
and Montgomery, 2003; Montgomery et al., 2006; Aberson et al., 2006). As
shown in Fig. 1, the azimuthal mean maximum wind speed does not show any jump
at 27 h, when there are 10 identified tornado-scale vortices. In the
following discussion, we will show that the mixing indeed exists, but its
effect on the azimuthal maximum wind speed cannot be detected. This is similar
to the conclusion from idealized numerical experiments conducted by Bryan
and Rotunno (2009). In fact, the azimuthal maximum wind speed (∼45 m s−1) is rather steady during the 10 h period after the
innermost domain has been activated for 2 h.

The number of the identified tornado-scale vortices is sensitive to the
threshold of vertical motion. If we relax the threshold of maximum vertical
motion to 15 m s−1, we can identify 89 tornado-scale vortices during
the 10 h period (Fig. 4a). Nearly all the tornado-scale vortices still occur
in the same semicircle of the enhanced eyewall reflectivity. This
relationship between the vertical wind shear orientation and the spatial
distribution of extreme updrafts is consistent with what Stern et al. (2016)
found from dropsonde observations in many storms. In our experiment, a few
variables are also stored at 3 s intervals during a 22 min period from the
31st hour. The duration of the tornado-scale vortex is examined in the 3 s
output. The duration is counted as the continuous period during which the
maximum vertical motion and vertical relative vorticity are not less than the
thresholds. For the thresholds of 20 m s−1 in vertical motion and
0.2 s−1 in vertical relative vorticity, the mean duration is 40 seconds
and the longest is 138 s. We can conclude that the identified tornado-scale
vortices are not repeatedly counted in the hourly output. The durations of
tornado-scale vortices are consistent with observational and numerical
studies (Wurman and Kosiba, 2018; Stern and Bryan, 2018).

Figure 4(a) Horizontal distribution of the tornado-scale vortices
identified with the thresholds of 15 m s−1 (yellow dots) and
20 m s−1 (red dots) in vertical motion and the Richardson number
(shading) averaged over 26–36 h; (b) the same as (a), but
for 27 h. The solid circle is the 500 m radius of maximum wind and dashed
circles indicate the distances from the TC center at 10 km intervals.

Figure 4a shows the location of the maximum vertical motions of the detected
tornado-scale vortices including 89 vortices identified with the threshold of
maximum vertical motion of 15 m s−1. Different criteria give a similar
distribution pattern of tornado-scale vortices; thus we just discuss the 24
tornado-scale vortices defined under the threshold of maximum vertical motion
of 20 m s−1 in the following discussion. The tornado-scale vortices
exclusively occur in the semicircle with intense convection from the
southeast to the northwest (Fig. 2a). Nearly all of the identified cases
occur in the inward side of the RMW or close to the
RMW (e.g., Stern et al., 2016; Stern and Bryan, 2018), with two exceptions
that are located outside of the RMW (Fig. 4a). One is M2901, which is
11.8 km from the RMW, and the other is M3601, which is 7.3 km from the RMW
(Table 1). Close examination indicates that these two tornado-scale vortices
occur between two high reflectivity bands (not shown).

Although the real tornado-scale vortices were observed by chance, they were
also associated with the intense radar reflectivity within the hurricane
eyewall and sharp horizontal reflectivity gradients (Aberson et al., 2006,
2017; Marks et al., 2008). In agreement with these studies, all of the
simulated tornado-scale vortices are associated with sharp horizontal
reflectivity gradients and most of them occur in the inner edge of the
intense eyewall convection within the RMW. As shown in Fig. 2a, all 10
cases at 27 h are located in the inner edge of the intense reflectivity. It
is suggested that the tornado-scale vortex favorably occurs at the inner edge
of the intense eyewall convection.

The gradient Richardson number (Ri) has largely been used as a
criterion for assessing the stability of stratified shear flow. It is defined
by

(1)Ri=N2S2,

where N2=g∂lnθe∂z is the
square of the Brunt–Väisälä frequency, S2=(∂u∂z)2+(∂v∂z)2 is the square of
vertical shear of the horizontal velocity, g is the gravity acceleration,
θe is the equivalent potential temperature, u is the
zonal wind speed, and v is the meridional wind speed. z is the vertical
coordinate. Using the smoothed fields, we also calculate the Richardson
number for each tornado-scale vortex (Table 1). It is calculated at each
level and then averaged over a layer between 200 and 800 m within a radius
of 1.5 km from the location of the maximum vertical motion. The Richardson
number is small, and it is negative for seven cases. As suggested by Stern et
al. (2016), the strong updraft is mainly within a kilometer of the surface
and it is implausible for buoyancy to be the primary mechanism for vertical
acceleration. In Fig. 4a, the Richardson number is also plotted, which is
averaged over the 10 h period. We can see that the tornado-scale vortices
generally occur in the areas with a Richardson number of less than 0.25. It is
indicated that the flow in these areas is dynamically unstable and turbulent.
The areas coincide with the semicircle of the enhanced eyewall convection.
Figure 4b further shows the field of the Richardson number at 27 h. The 10
tornado-scale vortices are all in an environment with a Richardson number of
less than 0.1. Since the Richardson number is calculated as the ratio of the
moist static stability to the vertical wind shear in the TCBL, we speculate
that the strong vertical wind shear in the inward side of the intense eyewall
convection is an important factor for the development of tornado-scale
vortices.

Figure 5 shows the vertical cross sections of tangential wind, radial wind,
vertical motion, reflectivity, and vertical relative vorticity below 2.5 km,
which are averaged in the northeast quadrant over a 10 h period. Note that
the radial locations of M2901 and M3601 are not shown in Fig. 5 due to the
effect of the limited innermost domain on the calculation of the azimuthal
mean. Note that there are relatively small changes in the RMW during the
10 h period. The maximum vertical motions associated with the tornado-scale
vortices are located inside the tilted RMW between the altitudes of 300
and 1300 m. Most of them (71 %) are found between 400 and 600 m. The
height of the maximum vertical motions becomes higher when the inflow layer
deepens outward. Figure 5b and c further indicate that the tornado-scale
vortices are generally found in the region of strong vertical motion averaged
over the northeastern quadrant, where the vortices are detected, and large
vertical relative vorticity with a sharp horizontal reflectivity gradient on
the inward side of the eyewall.

Using the high-resolution model output, we can explore the structural
features of the simulated tornado-scale vortex. After examination of all 24 identified tornado-scale vortices, we find that they can be
classified into three categories based on their vertical structure,
especially in terms of their vertical extent, stratification, and
near-surface wind jump.

Figure 6(a) The streamlines of the horizontal perturbation winds
for M2701 and the wind speed (shading) at the altitude of 10 m.
(b) The nearly vertical slice of the perturbation winds for M2701
with the red oval indicating the updraft–downdraft couplet. (c) The
streamlines of the three-dimensional perturbation wind for M2701. The warm
(cold) color of the streamline indicates the upward (downward) vertical
velocity perturbation and the vectors show the near-surface wind fields. The
vertical and horizontal axes indicate the altitude (km) from the surface and
the relative distances (km) from the nearest corner, respectively.

The first category includes 17 cases, accounting for 71 % of the total.
Their structural features can be represented by M2701, one of the four
strongest tornado-scale vortices, located 4.3 km inward from the 500 m RMW
(Table 1). In fact, the four strongest belong to the same category. In this
category, nearly all of the maximum vertical motions occur around the
altitude of 500 m, except M3001. The maximum vertical motion of M2701 is
31.98 m s−1 at the altitude of 400 m, while the maximum vertical
relative vorticity of 0.55 s−1 occurs at 200 m (Table 1). The 3-D
structure of the tornado-scale vortex can be clearly demonstrated by the
streamlines of perturbation winds near the strong updraft (Fig. 6). The flows
curl cyclonically upward from the surface (Fig. 6a). The tornado-scale vortex
is manifested by a small-scale circulation extending upward to ∼1.5 km. In addition, the tornado-scale vortex is closely associated with
updraft–downdraft couplets (Fig. 6b). Figure 6c shows that the tornado-scale
vortex is a complex twisted vortex system. The system has strong horizontal
circulation below 1 km and it turns into vertical circulation as the height
increases. So it contains both strong horizontal and vertical circulations.

Figure 7 shows the vertical cross section of vertical motion, equivalent
potential temperature, and simulated radar reflectivity along the line in
Fig. 3b for M2701. The inflow from the outward side and the outflow from the
eye side converge near the surface to the strong updraft that is below ∼1.5 km. On the top of the updraft, there is a layer of high equivalent
potential temperature (θe) (Fig. 7b). To the eye side
of the updraft, there is a high-θe layer below ∼1.5 km. The high-θe layer tilts upward and extends
outward. The large radar reflectivity can be found below the high-θe layer (Fig. 7c). The intense updraft is located in the
inner edge of the large radar reflectivity region. In addition, as suggested
by Aberson et al. (2006) and Marks et al. (2008), the strong updraft is
within a saturated layer (Fig. 8a), coinciding with high vertical relative
vorticity (Fig. 8c).

To the right of the updraft (Fig. 7b), another high-θe layer
can be seen at the altitude of ∼500 m. We check other cases in this
category of vortices and find that the lower-altitude high-θe layer is not always present. The downward motion at ∼500 m may be responsible for the lower-altitude high-θe
layer. The relatively low θe near the surface corresponds to
the inflow layer. The high-θe air meets with the cold inflow
air, resulting in relatively lower θe in the strong updraft.
It is indicated that the high-θe air in the eye is locally
entrained into the TC eyewall.

Some previous studies have shown that the quasi-linear bands are closely
associated with the horizontal rolls in the TC boundary layer, with
alternating upward and downward momentum transport on either side of the
rolls (Wurman and Winslow, 1998; Katsaros et al., 2002; Morrison et al.,
2005; Lorsolo et al., 2008; Ellis and Businger, 2010; Foster, 2013). To
demonstrate the relationship, Fig. 8b shows the radial profile of winds along
the line shown in Fig. 3b and the corresponding wind speeds at 10 and 400 m.
The figure clearly shows that the wind speed fluctuations at 10 m are
associated with the changes of the vertical motions in Fig. 7a. The wind
speed jump (Fig. 8b) is significant across the intense updraft (Fig. 7a). At
10 m, the wind speed suddenly increases from ∼30 to ∼60 m s−1. Note that the wind speed jump is larger at 400 m, ranging
from ∼35 to ∼95 m s−1. Marks et al. (2008) reported that
the wind speed at 450 m in altitude increased rapidly from <40 to
89 m s−1 in Hurricane Hugo (1989) when the NOAA research aircraft
encountered an EVM. We argue that the superposition of the horizontal
cyclonic circulation of the tornado-scale vortices plays an important role in
enhancing wind gusts on its radially outward side.

Figure 8(a) The radial–height cross section of perturbation winds
(vector) and relative humidity (shading) for M2701, (b) the 400 m
(blue) and 10 m (black) wind speeds, and the 400 m vertical relative
vorticity for M2701 along the line in Fig. 3b. The abscissa indicates the
relative outward distance.

There are three tornado-scale vortices in the second category, including
M2706, M2707, and M2708. The structural features can be represented by M2708.
In M2708, the maximum vertical motion and vertical relative vorticity occur
at 900 and 800 m, respectively (Table 1). The vertical motion of more than
8 m s−1 extends vertically from near the surface to ∼2 km
(Fig. 9a). In this category, we cannot see the warm air with high θe (Fig. 9b) and the strong updraft is located in a statically
unstable stratification (Table 1). The wind speed at the altitude of 900 m
varies by ∼20 m s−1 across the updraft, while the wind speed
gradient is relatively weak at 10 m (Fig. 9c).

The third category includes four cases: M2600, M2703, M2705, and M3002, in
which the updraft occurs in a statically stable stratification (Table 1).
Here we use M3002 as an example to show its vertical structure. As shown in
Fig. 10a, the updraft is elevated between 0.5 and 2 km. The maximum vertical
motion and relative vorticity are found at the altitude of 1300 m. In this
category, a pronounced feature is the deep low-θe (less than
364 K) layer in the inflow layer (Fig. 10b). As shown in Fig. 10c, the
gradient of the wind speed at 10 m is not clear while there is a speed jump
of ∼30 m s−1 in the vicinity of the updraft at 1300 m.

Previous studies suggest that the horizontal resolution should be below
100 m to simulate the development of 3-D turbulent eddies in the TCBL (Rotunno
et al., 2009; Green and Zhang, 2015). Based on our numerical experiment, the
tornado-scale vortex can be successfully simulated with the grids at the
resolution of 37 m. It should be noted that we have 12 vertical levels below
1 km. Vertical resolution in the innermost domain is relatively coarse
compared to the horizontal spacing of 37 m. We also conducted an experiment
(not shown) with the innermost domain resolution of 111 m. In this
experiment, the vertical resolution and horizontal resolution are comparable
in the TC boundary layer, and the tornado-scale vortices can also be found in
the experiment. At this time, we are not sure if these three categories
represent different phases in the life cycle of these coherent structures,
and since the 3 s output does not contain the thermodynamic variables, we
cannot examine the hydrostatic stratification.

A tornado-scale vortex or EVM in the TCBL has been observed in intense
hurricanes and is always associated with strong turbulence. To understand the
complicated interactions of the large-scale background flow, TC vortex,
mesoscale organization, and fine-scale turbulent eddies, a numerical
experiment in which a TC evolves in a typical large-scale background over the
western North Pacific is conducted using the WRF–LES framework with six
nested grids. The simulated tornado-scale vortex shows features similar to
those revealed with limited observations. It is suggested that the WRF–LES
framework can successfully simulate the tornado-scale vortex with the grids
at the resolution of 37 m that covers the TC eye and eyewall.

Following Wu et al. (2018), the tornado-scale vortex can be defined as a
small-scale cyclonic circulation with a maximum vertical motion of no less
than 20 m s−1 and maximum vertical relative vorticity no less than
0.2 s−1. A total of 24 tornado-scale vortices can be identified at the
11 hourly output times. Nearly all of them are within or close to the RMW.
Most of them occur in the inward side of the intense eyewall convection,
mostly below the altitude of 2 km. Tornado-scale vortices are mostly in
neutral or stable stratification within the saturated
high-θe layer. The tornado-scale vortex generally occurs in
the areas with a Richardson number of less than 0.25. We speculate that the
strong vertical wind shear in the inward side of the intense eyewall
convection is an important factor for the development of tornado-scale
vortices.

The simulated tornado-scale vortex has a small horizontal scale of 1–2 km
in the TCBL. It is accompanied by strong updrafts and a cyclonic circulation
with large vertical components of relative vorticity. The tornado-scale
vortex is closely associated with horizontal rolls. In nearly all of the
simulated tornado-scale vortex cases, the narrow intense updraft is coupled
with the relatively broad downdraft (figures not shown), constituting an
updraft–downdraft couplet or horizontal rolling vortex, as observed by the
research aircraft. Since the tornado-scale vortex is associated with intense
updrafts and strong wind gusts, its presence can pose a severe threat to the
eyewall penetration of manned research aircraft, and the strong wind gusts
associated with tornado-scale vortices can pose a severe risk to coastal life
and property.

We thank Ping Zhu of Florida International University for aiding with the
WRF–LES framework. This research was jointly supported by the National Basic
Research Program of China (2015CB452803), the National Natural Science
Foundation of China (41730961, 41675051, 41675009), and Jiangsu Provincial
Natural Science Fund Project (BK20150910). The numerical simulation was
carried out on the Tianhe Supercomputer, China.

The tornado-scale vortex in the tropical cyclone boundary layer has been speculated in intense hurricanes. A numerical experiment is conducted using the Advanced Weather Research and Forecast model by incorporating the large-eddy simulation technique. The simulated tornado-scale vortex shows the similar features as revealed with the limited observational data. The presence of the tornado-scale vortex also leads to significant gradients in the near surface wind speed and wind gusts.

The tornado-scale vortex in the tropical cyclone boundary layer has been speculated in intense...